164 
ete. We know then at once to what series they belong, and so what 
place they occupy in the whole system. If a meeting as discussed 
above should not take place for a line, we should consider that the 
line may belong to a series for which no other member has been 
found as yet for that element. Then the whole system of asymptotes 
(Pa Pee FSS Oger DS DG sen seul dhe ray Naer 
which the templet should be made to run successively along these 
asymptotes, in which way it is easy to find to what asymptote the 
considered line belongs. From the X-translation, which the templet 
then has, one can derive at once to what translation group the series 
belongs. In this way our pattern curve can be very serviceable in 
detecting and arranging new lines. - , 
I should like to.draw attention to another point. When we draw 
the systems of series for the different elements (I have, of course, 
only been able to select one for the adjoined plate), all kinds of 
different types" are found. Gradual changes take place when we 
proceed from one element to another in the same column of the 
table of Mexrpereserr, and also when we pass on to the other columns, 
the occurring changes in the type are very great. | bope to publish 
the results of a more extensive study on these changes later on. 
I] will make some remarks about this already here. On the 
annexed plate we find e.g. the asymptote S, of the P series lying 
above the P, asymptote of the S and D series. We also see that 
S, P, is pos. and P, S, neg. for «= 1. The absolute value of the two 
ordinates is the same. 
We find the same behaviour in the systems for the other alkali- 
metals, and also H, He, and OV. If we compare this with a diagram 
of the Thallium system or some other heavy metal, we observe 
exactly the reverse. Now the S, asymptote of the Pseries lies under 
the P, and P,’ asymptotes of the two components of the S and D 
series. Moreover S, P, and S, P,’ are now negative and P, S, and 
P.’ S, are the same, but positive. I will not enter just now into 
other points of difference between the two types. I will only draw 
attention to the following points: 
As appears from the diagram, the negative frequencies naturally 
occur here. So, as we are here almost compelled by the principle 
of continuity, to assume negative frequencies, [ consider the objections, 
entertained by Mocrnporrr *) against formulae with negative frequen- 
cies, entirely unfounded. 
In the same way the objection that Mocgrenporrr*) advances to the 
') Thesis for the doctorate, Amsterdam, p. 39. 
a) “ide: eit. ap. "39. 
